Landahl has submitted his retrial application to the Umeå court of appeals.
"Well, I have never experienced it before," Landahl told daily newspaper Norrländska Socialdemokraten, about applying for a retrial as the prosecutor and not the defence.
Quick has previously had three of his eight murder convictions overturned after withdrawing his confessions.
Christer Van Der Kwast, the former director of the Public Prosecution Authority, said that circumstantial evidence, such as a confession, cannot be wholly discounted.
"It would be strange to claim that someone cannot be convicted on circumstantial evidence because many people are serving jail sentences for that reason," Van Der Kwast told TT.
"Instead, the question that should be asked is whether the circumstantial evidence is strong enough," he said.
Bengt Landahl is expected to apply for another retrial in for Quick in the coming week. That case concerns a Dutch couple that was murdered while camping in northern Sweden in 1984.